Econ Grapher

Interest

What is Interest?
Interest is the fee that is paid from the borrower to the lender of an asset (usually monetary in nature). For example in the case of a loan of money, the borrower pays the original amount of money (the principal), and a fee for the use of the money (interest). Interest compensates the lender for the use of their assets, the opportunity cost (e.g. the profits foregone from investing the money elsewhere, or using it for something else e.g. consumption), and of course for credit risk i.e. the risk that the principal is not paid back in full. Interest more or less forms the basis of the banking business model (of borrowing at a rate that is lower than the rate earned on re-lending that money to another borrower).

How does it relate to Markets?
Interest is a fundamental concept in markets, it is a key input in valuation, investment decisions, asset pricing, derivative pricing, bond prices, credit risk measures, risk appetites, and even the health of the overall economy. Some general rules of thumb: higher interest rate = lower investment in stocks, lower valuations, lower bond prices, slower economy, and possibly reflects higher inflation, however it also means you get a higher return on money that earns interest at the higher rate. 

Calculation
Interest is typically calculated using an interest rate. An interest rate is a percentage that is applied to the principal e.g. 5.00% on $100 would be $5. To calculate the interest rate for a given period the formula is interest received divided by principal [so 5/100=0.05 (x100=5%)]. Another important aspect is the period to which the interest rate applies e.g. monthly, annual, etc. This also plays into whether the rate is the effective rate or advertised rate, for example an annual interest rate of 5% which is calculated based on the daily balance and paid monthly will see a higher effective rate.

Compounding
As hinted upon, when interest is allowed to compound, the effective interest rate becomes altered. In the Example of a 5% annual interest rate which is calculated daily and paid monthly the annual effective interest rate would be = [(1+(0.05/12))^12]-1 = 5.1162%. To calculate how interest will compound over time the general formula is FV = (1+rt)^t x P ...where FV = Future Value, rt = interest rate in period t (e.g. 1 year), t = compounding periods, and P = initial principal. So for example $100 compounded at 5% interest for 50 years would be FV = (1+0.05)^50 x 100 = $1,146.74. Thus is the magic of compounding interest.

Sources and further reading:
Wikipedia on Interest
Investor Words on Interest
Business Dictionary on Interest
Investopedia on Interest
wikinvest on Interest
Also see any elementary finance or economics textbooks

Graph Library:
Metric - Interest rates

Original Source: http://www.econgrapher.com/encyclopedia-interest.html

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